On spectral bounds for cutsets

Let be a simple and connected graph. A k-vertex separator [k-edge separator] is a subset of vertices [edges] whose deletion separates the vertex [edge] set of into two parts of equal cardinality, that are at distance greater than k in . Here we investigate the relation between the cardinality of these cutsets and the laplacian spectrum of . As a consequence of the study, we obtain the well-known lower bounds for the bandwidth and the bipartition width of a graph. c © 2002 Elsevier Science B.V. All rights reserved.